Question

1. geometry the width of a box is 2 m less than the length. the height is 1 m less than the length. the volume is 60 m³. what is the length of the box?

Explanation:

Step1: Define variables

Let length be \( l \, \text{m} \), width \( w = l - 2 \, \text{m} \), height \( h = l - 1 \, \text{m} \).

Step2: Volume equation

Volume \( V = lwh = 60 \), so \( l(l - 2)(l - 1) = 60 \).

Step3: Expand and simplify

\( l(l^2 - 3l + 2) = 60 \Rightarrow l^3 - 3l^2 + 2l - 60 = 0 \).

Step4: Solve cubic equation

Test \( l = 5 \): \( 5^3 - 3(5)^2 + 2(5) - 60 = 125 - 75 + 10 - 60 = 0 \). Root \( l = 5 \).

Answer:

5 m